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Wow! That is a lot of answers! This is gonna take a while to go through... thanks for all the answers so far!
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eidylonAug 25 '09 at 3:32

No soundcloud isn't the youtube of audio because it only lets you put x amount of storage and asks you to pay for more.
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user23373Aug 16 '12 at 0:19

You also can't update an existing track with a new one unless you pay them money. It is a bad choice.
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MarkMar 5 at 21:05

While SoundCloud isn't exactly a match, it certainly is the closest to YouTube you'll probably find on the Internet in terms of adoption and selection. There are many smaller such sites out there, but they don't have nearly as many songs (well known or not) on them.
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Caleb XuApr 13 at 1:04

+1 That was what I was thinking while reading the question
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fretjeAug 23 '09 at 22:23

You can actually provide the audio and in the mean time show some pictures rotating or something like that.
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fretjeAug 23 '09 at 22:24

4

Either pictures rotating (like a slideshow) or a fixed "title" screen detailing the name of the recording, date, etc. By the way, if you're going to upload church recordings to Youtube, you may want to disable posting comments. Take a look at any religious video's comments to see what I mean.
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T PopsAug 24 '09 at 14:52

I like drop.io for this purpose. I can't find any documentation of a length limit, but there may be one. Another option is to set up a tumbleblog on Tumblr. Then again you can also just use YouTube, adding a picture, although they have length limits.

Lala plays music, enables you to match your own music library (and upload the actual files if there's no match), and creates and maintains playlists. It's an iTunes-like interface, which is even more appropriate now that Apple control them (as of December 2009).

You didn't specify whether you wanted a strictly free site. Lala offers a lot for free, including uploading your own library, but adding new songs is 10 cents each and buying downloadable MP3s is around 79 cents each. Their download prices are competitive with Amazon MP3 and iTunes and are DRM-free, but be sure to check the encoding quality if that matters to you.

I would also add last.fm even though it is more like a personalised Internet Radio and doesn't work in every country anymore, but I still really like using it for discovering new Music and Events.

The problem is always the copyright thing (e.g. YouTube had trouble with the German Copyright Agency and now they must remove Music Videos under their license for German YouTube visitors... don't know if they actually did yet). Most services are only localised (like Pandora and Spotify mentioned by William). So probably YouTube is still the best and most popular source for playing Music.

One service that doesn't have that problem is Jamendo. It only offers music that is published under free licences. You won't find popular artists but browsing there might bring up some really cool stuff.